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The length of a rectangle is 9.7 cm more than 4 times the width. If the perimeter of the rectangle is 91.4 cm, what are its dimensions?
Let the width of the rectangle be x cm.
Therefore, the length of the rectangle is 4x + 9.7 cm.
The formula for the perimeter of a rectangle is P = 2(l + w), where P is the perimeter, l is the length, and w is the width.
Given that the perimeter is 91.4 cm, we can write the equation as:
91.4 = 2(4x + 9.7 + x)
91.4 = 2(5x + 9.7)
91.4 = 10x + 19.4
10x = 72
x = 7.2
So, the width of the rectangle is 7.2 cm and the length is:
4(7.2) + 9.7 = 28.8 + 9.7 = 38.5 cm
Therefore, the dimensions of the rectangle are 7.2 cm by 38.5 cm.